COURSE GOALS: Student should be introduced to a computer algebra system (like Sage, Ipython+modules, Mathematica, Maple or similar). He should be able to represent numerically and graphically mathematical objects from courses in mathematical analysis, linear algebra and mathematical methods of physics. He should be able to solve corresponding mathematical problems with one-line computer code and, if necessary, with more complex programming. Using these skills he should be able to simulate physical systems on a computer. Main goal of the course is to equip student with skills necessary for computer problem solving in the rest of his studies of physics.
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
2. APPLYING KNOWLEDGE AND UNDERSTANDING
2.3 apply standard methods of mathematical physics, in particular mathematical analysis and linear algebra and corresponding numerical methods
2.5 perform numerical calculation independently, even when a small personal computer or a large computer is needed, including the development of simple software programs
4. COMMUNICATION SKILLS
4.2 present one's own research or literature search results to professional as well as to lay audiences
4.3 develop the written and oral English language communication skills that are essential for pursuing a career in physics
5. LEARNING SKILLS
5.1 search for and use physical and other technical literature, as well as any other sources of information relevant to research work and technical project development (good knowledge of technical English is required)
5.4 participate in projects which require advanced skills in modeling, analysis, numerical calculations and use of technologies
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
After successfully finishing this course student will be able to
1. Perform calculations of standard problems from mathematical analysis and linear algebra (symbolic and numeric solving of normal and differential equations, symbolic and numeric integration and differentiation, manipulations with matrices and vectors) withing computer algebra environment.
2. Perform statistical analysis of data and fit parameters of models to data
3. Graphically represent functions or numerical arrays
4. Develop simple computer programs
5. Numerically simulate and graphically visualize simple physical systems.
1. Introduction to course and to computer algebra systems (3 hrs)
2. Interface 2.1 Worksheet and cells 2.2 Elementary calculations 2.3 Help system 2.4 Error messages (3 hrs)
3. Programming 3.1 Lists and other containers (6 hrs) 3.2 Flow control 3.3 Functions (3 hrs) 3.4 Plotting (4 hrs)
4. Mathematics 4.1 Symbolic expressions (2 hrs) 4.2 Equations (3 hrs) 4.3 Mathematical analysis (3 hrs) 4.4 Linear algebra (3 hrs) 4.5 Differential equations (5 hrs) 4.6 Statistics (2 hrs) 4.7 Fitting of model parameters to data (2 hrs)
5. Examples from physics: Mechanics (6 hrs)
REQUIREMENTS FOR STUDENTS:
Doing homeworks, online exams and final computer project.
GRADING AND ASSESSING THE WORK OF STUDENTS:
Students do homeworks and online exams (60 percent of grade), and a final project (40 percent of grade).